Table Of ContentVOLUME 1
APPLIED PHYSICS AND ENGINEERING
An International Series
Relaxation in Shock Waves
Relaxation
in Shock Waves
Yeo V. Stupochenko
S. A. Losev
and A. I. Osipov
Translated by
Scripta Technica, Inc.
Translation Editor
Richard Shao-lin Lee
College of Engineering
State University of New York
Stony Brook, New Yorh
SPRINGER-VERLAG • Berlin • Heidelberg • New York • 1967
Originally published under the title, Relaksatsionnyye Protsessy v Udarnykh
Volnakh, by Nauka Press, Moscow, 1965.
All rights reserved, especially that of translation into foreign languages. It is
also forbidden to reproduce this book, either whole or in part, by photo·
mechanical means (photostat, microfilm and/or microcard) or by other
procedure without written permission from the publishers.
ISBN 978-3-642-48248-9 ISBN 978-3-642-48246-5 (eBook)
DOI 10.1007/978-3-642-48246-5
© 1967 by Springer·Verlag New York Inc. Library of Congress Catalog Card
Number 67·21459.
Softcover reprint of the original edition 1967
Title No. 3891.
Translation Editor's Preface
This book by Yeo V. Stupochenko, S. A. Losev and A. I. Osipov distin-
guishes itself as an unusually comprehensive treatment of both the the-
oretical and experimental aspects of the subject of relaxation processes in
shock waves. S. A. Losev has done a considerable amount of work in molec-
ular absorption spectroscopy of gases in relaxation, and, consequently, the
chapter on experimental methods of study of nonequilibrium phenomena
in shock waves has turned out to be particularly extensive in both scope
and depth. A. I. Osipov has contributed extensively to the theoretical
understanding of relaxation processes in gases through his work on transi-
tion probability in nonadiabatic collisions by quantum-mechanical calcula-
tion as can be seen from the many quotations in the chapter on relaxation
processes in shock waves. Finally, Yeo V. Stupochenko's heavy contribution
to the development of the study of nonequilibrium gas flow must also be
mentioned, as it is obviously reflected at various places throughout the book.
It is worth particular mention that the authors have compiled the most
extensive bibliography of references (over six hundred in total) in the litera-
ture of relaxation gasdynamics to date. The authors' thorough familiarity
with the Western (particularly American) work in this ,!rea can be seen from
the many Western reference"~quoted, about two-thirds of the total number.
On the contrary, most of the more than two hundred Russian references are
not popularly known in the West and, therefore, should be of value to the
English-speaking readers.
A number of misprints found in the original Russian edition of this book
have been corrected in the English translation, and, for the convenience of
the English-speaking readers, the appropriate information on the origins of
quoted Western references or the English versions of quoted Russian re-
ferences, wherever available, has been added in the bibliography.
Stony Brook, October 1966 RICHARD SHAO-LIN LEE
v
Foreword
This book surveys the present state of the theory of relaxation processes
occurring in shock waves and in gases, and reviews the experimental ac-
complishments in this area.
When the shock wave was introduced into gasdynamics, it was viewed as
the surface of a discontinuity separating two gas regions in thermodynamic
equilibrium with each other. This concept of the shock wave has remained
valid for the overwhelming majority of problems and is applicable in those
cases where the actual thickness of the wave is small by comparison with the
flow dimensions. However, it may not hold with high-amplitude shock
waves in rarefied gases where the thickness of the shock wave becomes of
the same order as the dimensions of the streamlined body or the character-
istic dimensions of the fluid flow. In these cases the structure of the shock
wave and the processes which take place in it assume fundamental im-
portance.
Until recently, these processes were of only academic interest but are now
attracting much attention because of the burgeoning growth of aerospace
sciences and resultant demands on high-velocity gasdynamics. The intensive
studies of shock waves produced experimental techniques which (as it
frequently happens in science) find much wider application than in the
original problem of simulating flow past solid bodies at high altitudes. In
addition, the results of these specialized studies on ultrafast processes in
shock waves have been found pertinent to a great variety of other sciences,
from ultrasonics and optics to chemical kinetics.
We now have several recent books on the use of shock waves for studying
physicochemical processes (Ya. B. Zel'dovich and Yu. P. Rayzer, Physics
of Shock Waves and of High-Temperature Gasdynamics Phenomena, 1963
(1966); E. F. Green and 1. P. Teonnies, Chemische Reaktionen in Stosswellen,
Darmstadt, 1959; 1. N. Breadley, Shock Waves in Chemistry and Physics,
London, 1962; A. G. Gaydon and I. R. H urle, The Shock Tube in High-
Temperature Chemical Physics, London, 1963). However, none of these has
treated relaxation processes in shock waves exhaustively, a lack which this
book attempts to remedy. We shall concentrate on the physics of the relaxation
vii
viii Relaxation in Shock Waves
phenomena and, in particular, on the relationships governing the individual
processes involved in establishing statistical equilibrium at various degrees
of molecular freedom, as well as the kinetics of thermal dissociation and
ionization. These processes are fundamental to strong shock waves where
the temperatures may reach ten to twenty thousand degrees. By contrast,
we shall not dwell on the many applications of relaxation phenomena in
chemical physics, gasdynamics, etc. We shall discuss radiation of non-
equilibrium zones behind a shock front only briefly and shall not deal
with propagation of shock waves in plasma, a problem beyond the scope
of this book.
The first chapter presents basic theory: the formation and structure of
shock waves, the qualitative view of relaxation processes in gases, and the
theory underlying experimental techniques for study of these processes.
The following three chapters are devoted to relaxation processes in shock
waves. Here the authors tried to deal as comprehensively as possible with
the main directions, techniques and results of experimental and theoretical
studies in this field. The fifth chapter is devoted to the important practical
problem of nonequilibrium phenomena behind a shock front in air.
The motion of the gas in the relaxation zone of a shock wave, as any
other flow in which the dimensions of the relaxation zone are of the same
order as the characteristic flow length, is described by "relaxation" gas-
dynamics. The full treatment of the problems is beyond the scope of this
book, and the sixth (final) chapter is merely a brief survey of the flow prop-
erties of a gas undergoing relaxation.
We hope that this volume will be useful to working scientists in physical
gasdynamics, high-temperature physics, chemical physics, and students in
these disciplines.
The authors are deeply indebted to N. A. Generalov, Yu. P. Rayzer and
Yeo V. Samuylov for their valuable suggestions, as well as to all colleagues
who have helped in writing this book.
Contents
Translation Editor's Preface v
Foreword vii
Chapter 1. Experimental Study of Shock-wave Structure
[1] Creation and Structure of Shock-Waves . 1
[1] Introduction . 1
[2] Origin of the Discontinuity in an Ideal Fluid. The Hugoniot
Curve . 3
[3] Dissipative Processes in Shock Waves. 8
[4] Shock Waves in Multiatomic Gases 16
[2] Relaxation Processes in Gases (Elementary Theory) 20
[1] Establishment of the Maxwellian Distribution 21
[2] Excitation of Rotational Degrees of Freedom 23
[3] Excitation of Vibrational Degrees of Freedom 26
[4] Molecular Dissociation and Ionization 32
[5] Sequence of Relaxation Processes in Shock Waves 35
[3] Experimental Study of the Shock-wave Structure. 37
[1] Obtaining the Shock Wave. Simplified Theory of the
Shock Tube 37
[2] The Quantities Being Measured. 43
[3] Measuring Methods . 45
Chapter 2. The Shock Tube
[4] Methods of Obtaining Strong Shock Waves 49
[5] Gasdynamic Flows in Shock Tubes 61
[6] Inhomogeneity of the Flow Behind the Shock Front 72
[1] Inhomogeneity of the Flow Along the Plug 73
[2] Multidimensionality of the Flow 80
[3] Heat Transfer by Radiation. 89
[7] Auxiliary Measurements of Flow Variables in Shock Tubes 91
ix
x Relaxation in Shock Waves
[1] Measuring the Shock-wave Velocity 91
[2] Measuring the Initial Pressure and Temperature 98
[3] Preparing the Test Gas . 100
Chapter 3. Experimental Methods of Study of Nonequili-
brium Phenomena in Shock Waves
[8] General Requirements of the Recording Apparatus 104
[9] Certain Relationships for the Flow of Nonequilibrium Gas. 110
[10] Measuring the Gas Density. 117
[1] Study of the Reflection of Light from a Shock Front 117
[2] The Tepler Shlieren Scheme 121
[3] The Interferometer Method 126
[4] The Electron Beam Method 133
[5] The Use of X-ray Radiation 136
[11] Absorption Methods of Molecular Concentration Measurement 138
[1] Dependence of the Absorption on the Molecular
Concentration 140
[2] The Ultraviolet Spectral Region 143
[3] Determining the Relaxation Time and Dissociation Rate 148
[4] The Visible Spectral Region. 157
[12] Optical Study of Gases . 163
[1] Dependence of the Radiation on the Concentration of the
Gas Components . 163
[2] Recording Methods and Some Results 168
[3] Temperature Measurement . 174
[13] Measuring the Electron Concentration 180
[1] The Methods of Probes . 180
[2] Microradiowave Techniques. 182
[3] The Magnetic Induction Method 188
[4] Using the Stark Effect 191
[5] Recording the Optical Radiation 193
[6] The Interferometer Method. 195
[14] Other Methods of Measurement 196
[1] Thermal Measurements . 197
[2] Chemical Analysis. . 198
[3] Gasdynamic Experiments 201
Chapter 4. Relaxation Processes in Shock Waves
[15] Establishing a Maxwellian Distribution 206
Contents xi
[16] Rotational Relaxation 215
[17] Vibrational Relaxation 225
[1] Kinetic Equations and the Transition Probabilities 227
[2] Vibrational Relaxation of Diatomic Molecules which
Comprise a Small Admixture in a Monatomic Gas . 243
[3] Vibrational Relaxation in Pure Gases and in Mixtures
with a Monatomic Gas . 251
[4] Vibrational Relaxation of a Mixture of Polyatomic Gases 267
[18] Thermal Dissociation Kinetics . 271
[1] Thermal Dissociation as Molecular Transition from the
Discrete to the Continuous Vibrational State. 275
[2] Thermal Dissociation in a Single-component System. 281
[3] Concurrent Consideration of the Thermal Dissociation and
Vibrational Relaxation of Diatomic Molecules 286
[19] Thermal Ionization Kinetics. 293
[20] "Nonequilibrium" Radiation of Gases Behind the Front of
Strong Shock Waves. 302
Chapter S. Nonequilibrium Phenomena in Shock Waves in Air
[21] High-temperature Thermodynamic and Optical Properties of Air 306
[22] Vibrational Relaxation . 313
[23] Chemical Reaction Kinetics. 322
[24] Thermal Ionization Kinetics and Nonequilibrium Radiation 341
Chapter 6. Flow of a Gas Undergoing Relaxation
[25] Introduction . 348
[26] Equations of Relaxation Gasdynamics. 349
[1] Gaskinetic Methods for'Obtaining Equations of
Equilibrium and Relaxation Gasdynamics. 349
[2] The Use of Methods of Thermodynamics of Irreversible
Processes . 352
[27] Certain Properties of the Motion of Fluids Undergoing
Relaxation. Transition to Equilibrium Gasdynamics. 358
[28] The Case of Several Nonequilibrium Parameters. 363
References . 365
Author Index 385
Subject Index 388
I
Experimental Study
of Shock-wave Structure
[1] CREATION AND STRUCTURE OF SHOCK WAVES
[1] Introduction
Phenomena to which this book is devoted are a result of two important
properties of moving gases: I) the "nonlinear" character of the flow, which
is expressed in nonlinearity of the basic differential equations of gasdynamics;
and 2) statistical inequilibrium, which is peculiar to a moving medium (ex-
cluding certain types of motion; for example, uniform translational motion
of the system as a whole in a homogeneous field of external forces).
Under certain conditions the nonlinear effects result in the appearance of
surfaces at which the flow variables, such as, the velocity, density, pressure,
etc., become discontinuous, even if the initial disturbance of the medium was
sufficiently smooth. The statistical inequilibrium takes on a particular, sharp-
ly expressed character near these discontinuity surfaces and determines the
complex structure of shock waves.
In hydronamics of an ideal fluid, shock waves are geometrical surfaces
separating two regions of thermodynamically equilibrium states of a medium.
It follows from the laws of conservation of mass, momentum and energy,
and from the second law of thermodynamics applied to the propagation of
such surfaces, that when a medium passes through a shock wave the entropy
increases in a jump. Thus, the dissipative processes which transform the
medium from one thermodynamic equilibrium state to another are localized
in the geometric surfaces of the discontinuity.
This idealized picture of shock waves and the dissipation processes bound
up with them is a result of approximations which serve as a basis of Euler's
equation for the motion of an ideal fluid. From the molecular-kinetic view-
point, the state at which a gas is at thermodynamic equilibrium is a state of
total statistical equilibrium, which includes equilibrium distribution of the
energy over all degrees of molecular, atomic, ionic and electronic freedom,
